Requested feature overview description.
allow implications to use the full might of tag search in their logic

Why would it be useful?
if you have a set of tags where another thing must be true if the tags are such, then tag the other
eg fur solo dragon -> furred_dragon
male -[other gender tags] sex duo -> male/male (etc for other pairings) (i know that sex isn't a req for pairing tags but it's easy to illustrate/imply)

What part(s) of the site page(s) are affected?
the wiki for tag implications? other than that none visually
the site internals are the more worrying part, i have no idea how much work this would need to make happen

(if this has been rejected previously i didn't know)

Something like that sounds a hell of a lot more complicated than it's worth

It's a lot of work, and it's especially vulnerable to bad tagging.

fur solo dragon -> furred_dragon might sound solid on paper, but there's quite a few problems in reality:

• There's some disagreement on this, but it's common for a multiple_images post to have solo when multiple characters appear in separate images (e.g. post #2208800 has six solo portraits)
• In a theoretical example, a dragon could be transformed into a goat (or any other furred species) in a sequence where no fur is visible on the dragon until it's fully transformed into a goat. The image is solo because only one character appears in the image, as both a dragon and a goat, but never a furred dragon.
• solo is frequently used in place of solo_focus by inexperienced taggers and the fur may actually be part of a background character. This one isn't such a problem because bad tagging is equally a problem with regular implications.

You could amend this to fur solo dragon -transformation -multiple_images but these sorts of implications would require a lot of thinking time to weed out any possible edge-case scenario when the staff already can't keep up with basic AIBUR requests.

Negating tags isn't really a viable option either, it's easy to forget to tag something and that could result in tags being implied improperly.